A Counterexample to a Conjecture of Barr
نویسندگان
چکیده
We discuss two versions of a conjecture attributed to M Barr The Harrison cohomology of a commutative algebra is known to coincide with the Andr e Quillen cohomology over a eld of characteristic zero but not in prime characteristics The conjecture is that a modi ed version of Harrison cohomology taking into account torsion always agrees with Andr e Quillen cohomology We give a counterexample De nitions and Notation Let A be a commutative algebra over a commutative ring k and let M be an A bimodule We denote k simply by Consider the Hochschild cochain complex Homk A n M where is the Hochschild coboundary
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